where \(\beta ^*\)  and \(\kappa ^*\)  are given by Eqs. (REF ) and (REF ), respectively.
As performed in Ref. [1]}, Monte Carlo simulation with this action can be carried out efficiently.
Because the Polyakov loop \(\hat{\Omega }\)  is the order parameter of the deconfinement transition of QCD in the heavy quark limit, incorporation of its effect into the configuration can lead to drastic improvements in the lattice study of the QCD phase transition.
In Ref. [1]}, it was shown that the configuration generated by Eq. (REF ) with the leading-order \(\beta ^*\)  and \(\kappa ^*\)  removes the overlapping problem in the reweighting to incorporate the next-to-leading order effect.
Effective inclusion of higher-order effect in the configuration will help achieving the high orders of the hopping-parameter expansion required in a study of \(\kappa _c\)  for large values of \(N_t\) , thus extending the scope of the hopping parameter expansion.
